Material removal model considering influence of curvature radius in bonnet polishing convex surface

The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.     

Experimental investigation and analytical modelling of the effects of process parameters on material removal rate for bonnet polishing of cobalt chrome alloy

Cobalt chrome alloys are the most extensively used material in the field of total hip and total knee implants, both of which need highly accurate form and low surface roughness for longevity in vivo. In order to achieve the desired form, it is extremely important to understand how process parameters of the final finishing process affect the material removal rate. This paper reports a modified Preston equation model combining process parameters to allow prediction of the material removal rate during bonnet polishing of a medical grade cobalt chrome alloy. The model created is based on experiments which were carried out on a bonnet polishing machine to investigate the effects of process parameters, including precess angle, head speed, tool offset and tool pressure, on material removal rate. The characteristic of material removal is termed influence function and assessed in terms of width, maximal depth and material removal rate. Experimental results show that the width of the influence function increases significantly with the increase of the precess angle and the tool offset; the depth of the influence function increases with the increase of the head speed, increases first and then decrease with the increase of the tool offset; the material removal rate increases with the increase of the precess angle non-linearly, with the increase of the head speed linearly, and increases first then decreases with the increase of the tool offset because of the bonnet distortion; the tool pressure has a slight effect on the influence function. The proposed model has been verified experimentally by using different Preston coefficients from literature. The close values of the experimental data and predicted data indicate that the model is viable when applied to the prediction of the material removal rate in bonnet polishing.     

Prediction of surface quality considering the influence of the curvature radius for polishing of a free-form surface based on local shapes

When machining a free-form surface automatically and digitally, especially in the case of sophisticated surface shapes, it is very difficult to control the surface quality, and thus sophisticated surfaces are usually polished using manual labor. Over the past few years, there has been little attention to the calculation of material removal depth models and construction of theoretical roughness models considering the influence of the curvature radius. Bonnet polishing can be automatically adapted to polish complex free-form surfaces. This paper explores key problems related to forecasting surface quality with respect to bonnet polishing of free-form surfaces. First, for the convex and planar sub-regions, this paper deduces the relationship expressing the maximum pressure distribution and the curvature radius, and presents a computational expression for material removal depth, taking into consideration the influence of the curvature radius. An expression is also deduced for the dwell time relationship between the adjacent processing points according to the experimental results pertaining to the material removal depth. From this, a theoretical roughness model is constructed that relates the bonnet curvature radius and the workpiece curvature radius. The validity of the experiments is summarized in the conclusion. The research findings provide a basic theory for the prediction of surface quality that can be automatically adapted to a free-form surface shape in bonnet polishing.     

计算机控制光学表面成形技术的驻留时间算法

为了提高镜片的加工精度与效率,利用计算机控制光学表面成形技术(CCOS)的抛光方法对光学镜片进行抛光全过程动态仿真。根据Preston方程建立材料去除函数模型,对抛光过程中压力、转速以及工件与抛光磨头相对半径比对抛光去除速率的影响进行分析。为建立球面镜片的动态全过程仿真,结合卷积原理,推导加工残余误差与去除函数和驻留时间三者间的线性关系,根据镜片的对称性,将元素个数从2m+1点简化为m+1点,以提高运算效率。最后为获得仿真最小残余误差,采用非负最小二乘法求解驻留时间。结果表明,材料去除速率函数类似于高斯分布,抛光后能使镜片面形误差收敛,对模拟表面进行仿真,半径为100mm的镜片其初始表面形貌粗糙度的均方根值从0.467μm收敛到0.028μm,轮廓最大高度从6.12μm收敛到1.48μm。对实测表面进行加工仿真同样令其表面形貌粗糙度的均方根值从3.007μm收敛到0.107μm,轮廓最大高度从160.73μm收敛到13.76μm,因此提出的驻留时间求解方法对于球面镜片抛光全过程动态仿真有一定的可行性。     

气囊抛光去除函数的数值仿真与试验研究

为提高光学元件的面形精度,提高加工效率,对超精密气囊抛光方法的去除函数进行了理论和试验研究.通过分析气囊抛光的原理,以Preston方程为基础,应用运动学原理推导了气囊抛光"进动"运动的材料去除函数,利用计算机仿真的方法,得到近似高斯分布的去除函数,通过仿真分析几个主要参数对"进动"抛光运动去除特性的影响,总结得到三点气囊抛光工艺过程中重要的结论.通过在一台超精密气囊式智能抛光机上的试验对比,两者吻合很好,并得到面形精度 RMS=0.012 6 μm的超精密的光滑表面,为开展气囊抛光的工艺研究提供了理论依据.     

抛光液pH值等对硬盘玻璃盘基片化学机械抛光的影响

随着硬盘存储密度的增大、转速的提高、磁头飞行高度的降低,对硬盘基板材料及基板表面质量提出了更高的要求。采用纳米SiO2作为抛光磨料,在不同抛光液条件下(pH值、表面活性剂、润滑剂等),对玻璃基片化学机械抛光去除速率和表面质量的变化规律进行了研究,并利用原子力显微镜(AFM)和光学显微镜观察了抛光表面的微观形貌。结果表明,玻璃基片去除速率在酸性、碱性条件下变化趋势相近,即随着pH值的升高,材料去除速率先增大后减小。加入一定量的表面活性剂和润滑剂使得去除速率有一定程度的下降,但是表面粗糙度明显降低,并且表面没有出现颗粒吸附现象。     

超声波磁流变复合抛光中几种 工艺参数对材料去除率的影响

提出了一种光学抛光的新方法——超声波磁流变复合抛光。介绍了该抛光方法的基本原理和实验装置,进行了超声波磁流变复合抛光实验,采用轮廓仪实测了光学玻璃超声波磁流变抛光材料去除轮廓曲线。通过该项工艺实验,研究了五种工艺参数(磁场强度、超声振幅、抛光工具头与工件的间隙、抛光工具头转速、工件转速)对光学玻璃材料去除率的影响。在一定实验条件下,获得的材料去除率为0.139 μm/min,并获得了超声波磁流变复合抛光工艺参数与材料去除率的关系曲线,得出了光学玻璃超声波磁流变复合抛光的材料去除规律。     

基于修正Preston方程的百页轮抛光材料去除深度建模

由于百页轮具有一定的柔性,故实际材料去除深度与名义抛光深度不一致,直接影响抛光效率及表面质量的控制。基于Hertz弹性接触理论建立了抛光接触区抛光压力和切削速度分布函数,并依据修正的Preston方程建立了材料去除深度模型,据此确定了影响材料去除深度的关键抛光工艺参数(磨粒粒度、主轴转速、百页轮变形量和进给速度),获得了百页轮抛光接触区的材料去除深度分布规律和关键抛光工艺参数对材料去除深度的影响规律。最后,通过模拟仿真和抛光实验验证了所建模型和影响规律的正确性,结果表明,该模型可以较好地预测百页轮柔性抛光的材料去除深度。     

Effect of machining characteristics on polishing ceramic blocks

In this study, experiments were conducted to examine the effects of polishing parameters such as polishing time, load, rotational speed, diamond size, and concentration when polishing ceramic blocks. It was shown that the material removal rate rises with the increase in polishing time from 20 to 30 min, but drops with the increase from 30 to 40 min. The material removal rate increases with an increase in the load, rotational speed, diamond size, and concentration, respectively. Within the range examined, the surface roughness improves with a longer polishing time, higher rotational speed, smaller diamond size, and lower concentration. The parallelism is highly dependent on the material removal rate. Three main failure mechanisms: cracks, deep pits, and fractures were observed.     

Optimization of the chemical mechanical polishing process for optical silicon substrates

Chemical mechanical polishing (CMP) experiments are performed to study the effects of four key process factors on the flatness and surface finish of the polished optical silicon substrates and on the material removal rate (MRR). The experimental results and analyses reveal that the pad rotational speed and polish pressure have significant effects on the MRR, the interaction of the polish head rotational speed and slurry supply velocity and the interaction of the polish pressure and polish head rotational speed have significant effects on the flatness, and the pad rotational speed has a significant effect on the surface roughness R _t of the optical silicon substrates polished. The optimal combination of the four factors investigated is a polish pressure of 9,800 Pa, a pad rotational speed of 20 rpm, a polish head rotational speed of 20 rpm, and a slurry supply velocity of 100 ml/min. A confirmation CMP experiment has been carried out using the optimal process parameter setting obtained from the design of experiments analyses. The goal to attain optical silicon substrates with nanometric surface roughness and micrometric flatness by an optimized CMP process with a high MRR simultaneously so as to reduce the polishing time to only 15 min from over 8 h has been achieved.     

RESEARCH ON POLISHING PROCESS OF A SPECIAL POLISHING MACHINE TOOL

In this paper, a serial-parallel hybrid special polishing machine tool based on the elastic polishing theory is developed, which is used for polishing mould surface by using bound abrasives. This machine tool mostly consists of parallel mechanism of three-dimensional moving platform, series rotational mechanism of two degrees of freedom and elastic polishing tool device. The parallel mechanism controls the spatial position of the polishing tool. The series mechanism controls the pose of the polishing tool. The elastic polishing tool system can realize active control by a pneumatic servo system and passive conformity by a spring. The main process parameters that have influence on surface roughness and polishing efficiency are tool speed, feed rate, force, pose angle and polishing number of times. Optimal combination of process parameters is presented by the Taguchi and grey relational analysis, which provide a choice of parameters as a basis for free-form surface polishing in practice.     

An experimental study on the correlation of polishing force and material removal for bonnet polishing of cobalt chrome alloy

Cobalt chrome alloys are the most extensively used biomaterials for manufacturing artificial prostheses, which need nanometer scale surface roughness and micrometer scale form tolerance to extend their lifespan in the tough environment of the human body. In order to machine bearing surfaces to sufficiently high accuracy, the way in which material is removed by the final finishing, such as bonnet polishing, must be completely understood. This study has experimentally investigated the influence of process parameters (precess angle, head speed, tool offset, and tool pressure) on the polishing forces as well as the material removal in bonnet polishing of a medical grade cobalt chrome alloy. Experimental results indicate that normal force increases with the increase in the precess angle, head speed and tool offset, but varies only slightly with the variation of the tool pressure. Tangential force increases with the increase in the precess angle and tool offset while it shows little variation with the change of the head speed and tool pressure. It is concluded that both normal force and tangential force can contribute to the material removal rate, but tangential force is found to be more correlated with the width of the influence function while normal force has a stronger correlation with the maximal height of the influence function.     

TWO STEPS CHEMICAL-MECHANICAL POLISHING OF RIGID DISK SUBSTRATE TO GET ATOM-SCALE PLANARIZATION SURFACE

In order to get atomic smooth rigid disk substrate surface, ultra-fined alumina slurry and nanometer silica slurry are prepared, and two steps chemical-mechanical polishing (CMP) of rigid disk substrate in the two slurries are studied. The results show that, during the first step CMP in the alumina slurry, a high material removal rate is reached, and the average roughness (Ra) and the average waviness (Wa) of the polished surfaces can be decreased from previous 1.4 nm and 1.6 nm to about 0.6 nm and 0.7 nm, respectively. By using the nanometer silica slurry and optimized polishing process parameters in the second step CMP, the Ra and the Wa of the polished surfaces can be further reduced to 0.038 nm and 0.06 nm, respectively. Atom force microscopy (APM) analysis shows that the final polished surfaces are ultra-smooth without micro-defects.     

大口径光学元件的机械手抛光

为满足大口径光学元件多模式组合加工技术(MCM)的需要,研制了JP-01型数控抛光机械手。该机械手采用柱坐标结构,ρ-θ极坐标运动方式,ρ、θ两轴联动完成MCM加工所需各种运动。运用齐次坐标变换理论和Preston方程,在分析机械手抛光过程中工件表面上任意一点的相对速度、压强及抛光时间的基础上,建立了机械手抛光的材料去除数学模型,同时求解了JP-01型机械手的位姿转换矩阵。运用所建立的数学模型对MCM加工中修正环带误差和局部误差时单个抛光盘常用运动模式的材料去除特性进行了计算机模拟。应用JP-01型机械手对一口径为240 mm,F数为1.5的球面反射镜进行了确定性抛光实验,最终面形精度达到14.6 nm(RMS)。实验表明,所测得数据与理论分析数据吻合,建立的数学模型能真实反映材料去除分布特性,可以指导抛光实现确定性加工,JP-01型机械手能够提供MCM加工所需运动形式。     

随动压力分布下的非球面抛光去除函数

考虑去除函数对数控小工具抛光光学元件精度的影响,提出了如何根据需要加工的非球面参数以及抛光盘参数得到最优去除函数的方法。由于计算非球面上去除函数的核心是准确获得抛光盘与镜面间的动态压力分布,本文提出利用有限元法仿真抛光盘与非球面间的压力分布,并结合经典Preston方程与行星运动模型来得到非球面不同位置处的去除函数。基于随动压力分布模型,分析了沥青盘抛光非球面时在不同抛光位置处去除函数的变化。在曲率半径为1 000mm的球面上进行了去除函数验证实验。结果表明:基于本文理论得到的去除函线型更接近实际情况,皮尔逊系数达到了0.977。本文提出的方法可以方便地调整加工位置来得到相应的压力分布,实现去除函数的优化,对提高加工效率与精度有实际指导意义。     

计算机硬盘基片的亚纳米级抛光技术研究

随着计算机磁头与磁盘间隙的不断减小,硬盘表面要求超光滑(亚纳米级粗糙度)。化学机械抛光技术是迄今几乎唯一的全局平面化技术。研究了抛光液特性与计算机硬盘基片的化学机械抛光性能间的关系,结果表明,抛光后表面的波纹度(Wa)、粗糙度Ra)以及材料去除量强烈依赖于抛光液中磨粒的粒径、磨粒和氧化剂的浓度等因素。借助对抛光后表面的俄歇能谱(AES)分析,对其化学机械抛光机理进行了探讨。     

Prediction of the surface roughness and material removal rate in chemical mechanical polishing of single-crystal SiC via a back-propagation neural network

Chemical mechanical polishing (CMP) is a common method for realising the global planarisation and polishing of single-crystal SiC and other semiconductor substrates. The strong oxidant hydroxyl radicals (·OH) generated by the Fenton reaction can effectively oxidise and corrode the SiC substrate, and are thus used to improve the material removal rate (MRR) and surface roughness (Ra) after polishing of SiC during CMP. Therefore, it is necessary to study the material removal mechanism in detail. Based on the modified Preston equation, the effects of the CMP process parameters on the MRR and Ra after polishing of SiC and their relationship were studied, and a prediction model of the CMP process parameters, MRR, and Ra after polishing was also established based on a back-propagation neural network. The MRR initially increased and then decreased, and the Ra after polishing initially decreased and then increased, with increasing FeSO₄ concentration, H₂O₂ concentration, and pH value. The MRR continuously increased with increasing abrasive particle size, abrasive concentration, polishing pressure, and polishing speed. However, the Ra continuously decreased with increasing abrasive particle size and abrasive concentration, increased with increasing polishing pressure, and initially decreased and then increased with increasing polishing speed. The established prediction model could accurately predict the relationship between the process parameters, MRR and Ra after polishing in CMP (relative prediction error of less than 10%), which could provide a theoretical basis for CMP of SiC.     

Modelling of the Polished Profile in Computer-Controlled Polishing by a Sub-Aperture Pad

High-quality part surfaces with high surface finish and form accuracy are increasingly in demand in the mold/die and optics industries. The computer-controlled polishing (CCP) is commonly used as the final procedure to improve the surface quality. This paper presents a theoretical and experimental study on the polished profile of CCP with sub-aperture pad. A material removal model is proposed based on the evaluation of the amount of material removed from the surface along a direction orthogonal to the tool path. The model assumes that the material removal rate follows the Peterson equation. The distribution of the sliding velocity at the contact region is presented. On the basis above, the approaches to calculate the polished profiles are developed for the sub-aperture pad polishing along a straight path and a curved path. The model is validated by a series of designed polishing experiments, which reveals that polishing normal force, angular spindle velocity, feed rate and polishing path all have effects on the polished profile. The result of experiments demonstrates the capability of the model-based simulation in predicting the polished profile.     

数字光盘玻璃基片的三步抛光技术

为得到超光滑的数字光盘母盘玻璃基片表面,研究玻璃基片的亚纳米级抛光技术。分别采用2 m、0.3 m超细氧化铈抛光液以及纳米氧化硅抛光液进行三步化学机械抛光(Chemical mechanical polishing, CMP),抛光后最终表面粗糙度Ra达到0.44 nm,为目前报道的数字光盘母盘玻璃基片抛光的最低值。原子力显微镜分析表明,抛光后的表面超光滑且无微观缺陷。通过对玻璃基片CMP中机械作用及化学作用进行分析,对抛光机理进行了探讨。     

Theoretical and experimental investigation of surface generation in swing precess bonnet polishing of complex three-dimensional structured surfaces

Three-dimensional structured surfaces (3D-structured surfaces) possessing specially designed functional textures are widely used in the development of advanced products. This paper presents a novel swing precess bonnet polishing (SPBP) method for generating complex 3D-structured surfaces which is accomplished by the combination of specific polishing tool orientation and tool path. The SPBP method is a sub-aperture finishing process in which the polishing spindle is swung around the normal direction of the target surface within the scope of swing angle while moving around the center of the bonnet. This is quite different from the ‘single precess’ and ‘continuous precessing’ polishing regime, in which the precess angle is constant. The technological merits of the SPBP were realized through a series of polishing experiments. The results show that the generation of complex 3D-structured surfaces is affected by many factors which include point spacing, track spacing, swing speed, swing angle, head speed, tool pressure, tool radius, feed rate, polishing depth, polishing cloth, polishing strategies, polishing slurry, etc. To better understand and determine the surface generation of complex 3D-structured surfaces by the SPBP method, a multi-scale material removal model and hence a surface generation model have been built for characterizing the tool influence function and predicting the 3D-structured surface generation in SPBP based on the study of contact mechanics, kinematics theory, abrasive wear mechanism, and the convolution of the tool influence function and dwell time map along the swing precess polishing tool path. The predicted results agree reasonably well with the experimental results.